Attention recently has been focused on developing materials capable of controlling the propagation of light in much the same way that semiconductors control the propagation of electrons. Over the past decade substantial progress has been made toward this goal and the new field of photonic crystals has emerged. A photonic crystal functions as a semiconductor for light in the sense that it possesses a photonic band gap that defines a range of electromagnetic frequencies that are unable to propagate in the crystal in one or more directions.
The ability of semiconductors to control the propagation of electrons originates from the periodic lattice arrangement of the atoms that constitute the semiconductor. The precise arrangement and spacing of atoms ultimately dictates the electronic potential that underlies the band structure, bandgap and electronic states of a semiconductor. Periodicity is also used in photonic crystals to achieve a photonic bandgap and to control the density of photonic states at different frequencies. Instead of a periodic electronic potential originating from periodically arranged atoms, however, periodicity of the refractive index originating from a periodic arrangement of one dielectric medium within another underlies the formation of a photonic bandgap. Since electromagnetic radiation of interest in photonic applications has a longer wavelength than the electrons confined in a semiconductor, the periodic spacing of the refractive index variation in a photonic crystal is larger than the periodic spacing of atoms in a semiconductor. When a photonic bandgap forms, the wavelengths of electromagnetic radiation within the bandgap are those that are comparable to the periodic spacing in refractive index. Electromagnetic radiation having an energy within the photonic band gap and propagating in a direction defined by the photonic band gap is blocked and unable to propagate in a photonic crystal. When external light having an energy and direction of propagation within the photonic band gap is made incident to a photonic crystal, it is unable to propagate through the crystal. Instead, it is perfectly reflected. Light with an energy or direction of propagation outside of the photonic band gap, on the other hand, freely passes through the crystal (subject, of course to ordinary absorption and reflection processes). This feature makes photonic crystals essentially perfect reflectors of incident wavelengths that are within the wavelength range and range of propagation directions encompassed by the photonic bandgap.
An example of a practical photonic crystal would be a material that consists of a flat dielectric slab that contains a periodic arrangement of holes extending in the thin direction and aligned along the lateral dimensions of the slab. Such a material may be viewed as a periodic arrangement of rods comprised of air and corresponds to a photonic crystal in which air is the macroscopic dielectric medium and the slab is the surrounding medium. Another example of a photonic crystal would be a periodic array of cylindrically shaped rods made of a dielectric material supported by a substrate with the space between the rods being filled by air or a dielectric material other than the one from which the rods are made. In this example, the rods correspond to the periodically distributed macroscopic dielectric medium and the material filling the space between the rods corresponds to the surrounding matrix. The precise details of the periodic pattern of rods (or other shape) and the refractive index contrast between the periodic macroscopic dielectric medium and its surroundings influences the properties of the photonic crystal.
Photonic crystals can be formed from a wide variety of macroscopic dielectric media provided that an appropriate refractive index contrast with a surrounding medium can be achieved. As an example, the composition of the holes or rods in the example above is not limited to air. Other materials that present a sufficiently large refractive index contrast with the surrounding flat dielectric slab may be used to form the rods. A periodic lattice of air holes, for example, may be drilled in a flat dielectric slab and subsequently filled with another material to form a photonic crystal. The rod material may have a higher or lower refractive index than the slab material. As another example, a periodic array of rods comprised of a macroscopic dielectric medium such as silicon in air as the surrounding medium represents a photonic crystal.
Important material design considerations include the size, spacing and arrangement of macroscopic dielectric media within a volume of surrounding material as well as the refractive indices of the dielectric and surrounding materials. The periodicity of the macroscopic dielectric media can extend in one, two or three dimensions. These considerations influence the magnitude of the photonic band gap, the frequency range of light or other electromagnetic energy (e.g. infrared, microwave etc.) that falls within the photonic band gap and whether the photonic band gap is full (in which case the photonic band gap effect is manifested regardless of the direction of propagation of the incident light) or partial (in which case the photonic band gap effect is manifested for some, but not all, directions of propagation). Other practical considerations are also relevant such as manufacturability, cost, ability to fabricate a periodic array of rods etc. Effects analogous to doping or defects in semiconductors may also be realized in photonic crystals. An inherent consequence of dopants or defects in semiconductors is a disruption or interruption of the periodicity of the lattice of atoms that constitute the semiconductor. The electronic states associated with dopants or defects are a direct consequence of the local disturbance in periodicity imparted to the semiconductor lattice. Photonic crystals can similarly be perturbed in ways analogous to introducing dopants and defects in semiconductors. Defects can be used to spatially confine light within a photonic crystal. A point defect can be used to localize electromagnetic radiation having a wavelength within the photonic bandgap. This occurs because the localized electromagnetic radiation is unable to escape from the defect due to its inability to propagate into or through the surrounding photonic crystal by virtue of the fact that the localized wavelength is within the photonic bandgap. Linear and planar defects can similarly be used to confine electromagnetic radiation in one or two dimensions within a photonic crystal.
The periodicity of a photonic crystal is a consequence of a regular and ordered arrangement of macroscopic dielectric media within a surrounding medium. Effects that interrupt the arrangement of macroscopic dielectric media can be used to break the periodicity to create localized or extended defect photonic states within the photonic band gap. Defects can be formed in rod array photonic crystals, for example, by perturbing one or more of the rods with respect to other rods in an array. Possible ways of perturbing rods in a surrounding dielectric slab, for example, include varying the size, position, optical constants, chemical composition of one or more rods or forming rods from two or more materials. Perturbation of a single rod provides a point defect that can be used to localize light. Perturbation of a row of rods provides a linear defect that acts to confine light in a channel. Such defects can be used to efficiently transfer light through the crystal without losses.
As the field of photonic crystals develops, the need for new photonic band gap materials is increasing. An important potential area of application for photonic crystals is waveguiding. In an ideal waveguide, a propagating beam of electromagnetic radiation is totally confined to a direction dictated by the waveguide. A three-dimensional photonic crystal offers an approach for achieving total confinement and lossless propagation of light. Waveguiding can be achieved in a three-dimensional photonic crystal by including a linear defect in the interior of the crystal. Light localized in the defect is confined to the defect if the wavelength is within the photonic bandgap of the surrounding photonic crystal. This occurs because the light is unable exit the defect and enter the surrounding photonic crystal. Three-dimensional photonic crystals are desirable for waveguiding applications because the photonic bandgap is complete in the sense that the effects of the photonic bandgap effects are manifest regardless of the direction of propagation of the light having a wavelength within the gap. Full three-dimensional confinement by the photonic bandgap over a full range of propagation directions is achievable and transmission losses are avoided. Three-dimensional photonic crystals are thus a highly valuable target for compact integrated optics systems which necessarily require sharp bends to minimize system size. In the absence of a three-dimensional photonic bandgap, prohibitive losses would occur at bends as the propagating light travels in a direction that fall outside of the bandgap.
A current outstanding problem, however, is the practical difficulty of achieving a full three-dimensional photonic crystal. A complete photonic bandgap requires the construction of a three-dimensional photonic crystal. The exacting requirements for periodically arranging macroscopic dielectric objects having a size on the order of the wavelength of propagating light has proven to be both challenging and costly.
A need exists for photonic crystals whose performance approaches that expected for three-dimensional photonic crystals and whose manufacture is less demanding. One solution that has been proposed is the slab photonic crystal. A slab photonic crystal includes a photonic crystal layer having a finite thickness and including a periodic array in two dimensions of one dielectric material within a surrounding dielectric material having a different composition. The layered structure of the slab photonic crystal makes its construction amenable to widely available layered deposition and processing techniques.
Periodicity in a slab photonic crystal occurs in the two lateral (in the plane of slab) dimensions, but is absent in the direction normal to the slab (i.e. thickness direction). Since a photonic crystal layer of this type is not periodic in three dimensions, it lacks a complete bandgap. This means that the photonic bandgap is operable with respect to included wavelengths only over a particular range of propagation directions. Wavelengths that are nominally within the bandgap are excluded from the bandgap for directions of propagation that fall outside of those encompassed by the bandgap. In this sense, the confinement of light by a defect in a photonic crystal layer is incomplete since the confinement is effective only for a limited range of propagation directions.
In a slab photonic crystal, the confinement of light is made complete by interposing a photonic crystal layer between two lower index dielectric cladding layers. The purpose of the cladding layers is to provide conventional index confinement of light that falls outside of the photonic bandgap of the photonic crystal layer. In this way, light can be maintained within the combination of layers without incurring substantial losses. The slab photonic crystal layer provides confinement for lateral propagation directions (directions of periodicity of the photonic crystal layer), while the cladding layer provides confinement in the slab normal direction.
A practical problem commonly encountered in the fabrication of slab photonic crystals is an asymmetry in the shape of the periodically arranged dielectric medium in the direction normal to the slab. In a typical example, the photonic crystal layer of a slab photonic crystal includes a periodic array of macroscopic rods comprised of a first dielectric material within a surrounding matrix of a second dielectric material. In the planar processing of such a photonic crystal layer, processing occurs by etching holes in a solid piece of the second (surrounding) dielectric material and subsequently filling these holes with the first dielectric material. Due to the nature of the etching process, the holes that form are not precisely cylindrical, but rather slightly conical or tapered so that the top of the hole is wider than the bottom part of the hole. The tapering is a consequence of the fact that the upper part of the hole is more readily accessed by the etchant, while the lower part of the hole is more difficult to access. Etching therefore occurs most efficiently at the top surface and becomes progressively less efficient due to inhibited access of the etchant away from the surface toward the bottom of the hole.
A consequence of the tapering is that the cross-sectional shape and/or area of the periodically arranged dielectric regions is non-uniform in the slab normal direction. This non-uniformity has a deleterious effect on waveguiding because it represents a destruction of mirror symmetry with respect to the mid-plane of the slab. This loss of symmetry leads to a mixing of guided modes of different parity and as a result, single mode waveguiding is precluded. Instead, mode coupling and multimode transmission occur with an accompanying increase in losses due to reflection. In order to improve the transmission efficiency of slab photonic crystals, it is desirable to devise a system that preserves mirror symmetry so that single mode operation can be achieved.